Removing redundancy for attribute implications in data with grades

Reasoning with if-then rules –in particular, with those taking from of implications between conjunctions of attributes– is crucial in many disciplines ranging from theoretical computer science to applications. One of the most important problems regarding the rules is to remove redundancies in order to obtain equivalent implicational sets with lower size.

CAISL: Simplification Logic for Conditional Attribute Implications

In this work, we present a sound and complete axiomatic system for conditional attribute implications (CAIs) in Triadic Concept Analysis (TCA). Our approach is strongly based on the Simplification paradigm which offers a more suitable way for automated reasoning than the one based on Armstrong’s Axioms. We also present an automated method to prove the derivability of a CAI from a set of CAI s.